Leigh Griffiths’ strike after 36 minutes gave the Ladbrokes Premiership leaders a deserved victory and confirmed the best domestic start by a new Parkhead manager, who is unbeaten in 19 games in Scotland.
The champions moved 11 points clear of Rangers with two games in hand but Rodgers, who has already won the BetFred Cup in his first season in charge, was keen to play down his part.
He said: “It is very nice, it is a great mark of the players’ concentration, how relentless they have been to keep going. The point I make to them is very simple.
“When you are winning, the attitude is very simple, work like you are losing and keep working and be relentless and if you are going to succeed you have to have drive and desire.
“You need many qualities to keep winning but two of the biggest one is that drive determination and hunger and we show that in bucket loads.”
Middlesbrough climbed into the Sky Bet Championship play-off positions as Patrick Bamford's first career hat-trick secured a comfortable 3-0 win over Leeds.
Louis Longridge and Greg Docherty will leave friendship at the side of the pitch for 90 minutes on Sunday when Falkirk face Rangers at Ibrox.